Advanced Search
MyIDEAS: Login to save this article or follow this journal

Rates of consistency for nonparametric estimation of the mode in absence of smoothness assumptions


Author Info

  • Herrmann, Eva
  • Ziegler, Klaus
Registered author(s):


    Nonparametric estimation of the mode of a density or regression function via kernel methods is considered. It is shown that the rate of consistency of the mode estimator can be determined without the typical smoothness conditions. Only the uniform rate of the so-called stochastic part of the problem together with some mild conditions characterizing the shape or "acuteness" of the mode influence the rate of the mode estimator. In particular, outside the location of the mode, our assumptions do not even imply continuity. Overall, it turns out that the location of the mode can be estimated at a rate that is the better the "peakier" (and hence nonsmooth) the mode is, while the contrary holds with estimation of the size of the mode.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 68 (2004)
    Issue (Month): 4 (July)
    Pages: 359-368

    as in new window
    Handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:359-368

    Contact details of provider:
    Web page:

    Order Information:

    Related research

    Keywords: Nonparametric curve estimation Mode Kernel smoothing Rates of consistency Nonsmooth curves;


    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Vieu, Philippe, 1996. "A note on density mode estimation," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 297-307, March.
    2. Joseph Romano, 1988. "Bootstrapping the mode," Annals of the Institute of Statistical Mathematics, Springer, vol. 40(3), pages 565-586, September.
    3. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    Cited by:
    1. Shi, Xiaoping & Wu, Yuehua & Miao, Baiqi, 2009. "A note on the convergence rate of the kernel density estimator of the mode," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1866-1871, September.
    2. Salah Khardani & Mohamed Lemdani & Elias Ould Saïd, 2012. "On the strong uniform consistency of the mode estimator for censored time series," Metrika, Springer, vol. 75(2), pages 229-241, February.
    3. Obereder, Andreas & Scherzer, Otmar & Kovac, Arne, 2007. "Bivariate density estimation using BV regularisation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5622-5634, August.


    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:359-368. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.